Sharing a Measure of Maximal Entropy in Polynomial Semigroups

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Let P1, P2, . . . , Pk be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or to Chebyshev polynomials, and S the semigroup under composition generated by P1, P2, . . . , Pk. We show that all elements of S share a measure of maximal entropy if and only if the intersection of principal left ideals SP1 ∩ SP2 ∩ · · · ∩ SPk is non-empty.

Original languageAmerican English
Pages (from-to)13829-13840
Number of pages12
JournalInternational Mathematics Research Notices
Issue number18
StatePublished - 1 Sep 2022

All Science Journal Classification (ASJC) codes

  • General Mathematics


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